Reorientational time

FIG. 4 Dependence of molecular reorientation times of benzene on the concentration of polystyrene denotes the parallel ( frisbee ) mode, the perpendicular ( tumbling ) mode [26]. 

Spohr found a significant reduction in the dipole reorientation time for a different model of water (but using the same water/Pt potential). In that paper, the reorientation dynamics are characterized by the spectral densities for rotation around the three principal axes of the water molecule. These calculations demonstrated the hindered rotation of water molecules in the plane parallel to the surface. In addition, a reduction in the frequency of rotation about the molecular dipole for water molecules in the adsorbed... 

In order to obtain information on the electron relaxation time in copper aqua ion, measurements should not be performed in water solution, because the correlation time for proton relaxation is in that case the reorientational time, which is much smaller than T g. NMRD profiles should be actually acquired in ethylene glycol solution and at temperatures lower that room temperature, so that the reorientational time increases one two orders of magnitude (see Section II.B). In this way T e of the order of 10 s can be estimated. 

No field dependence in the electron relaxation time was ever found in the investigated region between 0.01 and 100 MHz of proton Larmor frequency, or at 800 MHz when high resolution is achieved (28). It was shown that Tie is essentially independent of the reorientational time of the macromolecule and the viscosity of the solution. Therefore, rotation independent mechanisms have to be operative. We also find that Tie decreases with increasing temperature, as also shown in Fig. 5. 

The NMRD profile of Mn(H20)g in water solution shows two dispersions (Fig. 10) in the 0.01-100 MHz range of proton Larmor frequency one, at about 0.05 MHz, due to the contact relaxation, and a second, at about 7 MHz, due to the dipolar relaxation (39). The correlation time for contact relaxation is the electron relaxation time, whereas the correlation time for dipolar relaxation is the reorientational time (ir = 3.2 x 10 , in accordance with the value expected for hexaaquametal(II) complexes). This accounts for the different positions of the two dispersions in the profile. From a best fit of longitudinal and transverse proton relaxation profiles, the electron relaxation time is described by the parameters A = 0.02-0.03 cm and... 

Chromium(III) has a ground state in pseudo-octahedral symmetry. The absence of low-lying excited states excludes fast electron relaxation, which is in fact of the order of 10 -10 ° s. The main electron relaxation mechanism is ascribed to the modulation of transient ZFS. Figure 18 shows the NMRD profiles of hexaaqua chromium(III) at different temperatures (62). The position of the first dispersion, in the 333 K profile, indicates a correlation time of 5 X 10 ° s. Since it is too long to be the reorientational time and too fast to be the water proton lifetime, it must correspond to the electron relaxation time, and such a dispersion must be due to contact relaxation. The high field dispersion is the oos dispersion due to dipolar relaxation, modulated by the reorientational correlation time = 3 x 10 s. According to the Stokes-Einstein law, increases with decreasing temperature, and... 

Alternatively, in order to take into account the effects of rotational diffusion of a water molecule around the metal-oxygen axis, a rotational correlation time for the metal-H vector was considered as an additional parameter besides the longer overall reorientational time 82). 

When the temperature is lowered and/or the viscosity of the solution is increased by using glycerol-water mixtures as solvent, the reorientational correlation time increases. Since the reorientational time is the correlation time for nuclear relaxation, the effects on the NMRD profile (Pig. 27) are (i) higher relaxivity values at low frequencies (ii) a shift toward lower... 

The NMRD profiles of V0(H20)5 at different temperatures are shown in Fig. 35 (58). As already seen in Section I.C.6, the first dispersion is ascribed to the contact relaxation, and is in accordance with an electron relaxation time of about 5 x 10 ° s, and the second to the dipolar relaxation, in accordance with a reorientational correlation time of about 5 x 10 s. A significant contribution for contact relaxation is actually expected because the unpaired electron occupies a orbital, which has the correct symmetry for directly overlapping the fully occupied water molecular orbitals of a type (87). The analysis was performed considering that the four water molecules in the equatorial plane are strongly coordinated, whereas the fifth axial water is weakly coordinated and exchanges much faster than the former. The fit indicates a distance of 2.6 A from the paramagnetic center for the protons in the equatorial plane, and of 2.9 A for those of the axial water, and a constant of contact interaction for the equatorial water molecules equal to 2.1 MHz. With increasing temperature, the measurements indicate that the electron relaxation time increases, whereas the reorientational time decreases. 

The NMRD profile of bis-oxovanadium(IV) transferrin displays two dispersions (Fig. 36) (59). The one at about 10 MHz is attributed to the co/ dispersion, providing in this way a value for equal to 2 x 10 s, which is ascribed to the electron relaxation time with possible contributions from tm, since the reorientational time of the protein is of the order of 2-3 x 10 s. The fit requires considering the presence of hyperfine coupling with... 

Interestingly, the reorientational time is about 2-3 times larger than expected for a hexaaqua ion. Indeed, the second sphere water molecules... 

The presence of second-sphere water molecules could be considered also for other metal aqua ions, like iron(III) and oxovanadium(IV) aqua ions, where the reorientational time is found to be longer than expected. However, in the other cases increases much less than for the chromium(III) aqua ion, thus suggesting that second-sphere water molecules are more labile, their lifetime being of the order of the reorientational time. 

As an example of behavior of a typical Gd-complex and Gd-macromolecule we discuss here the NMRD profiles of a derivative of Gd-DTPA with a built-in sulfonamide (SA) and the profile of its adduct with carbonic anhydrase (see Fig. 37) 100). Other systems are described in Chapter 4. The profile of Gd-DTPA-SA contains one dispersion only, centered at about 10 MHz, and can be easily fit as the sum of the relaxation contributions from two inner-sphere water protons and from diffusing water molecules. Both the reorientational time and the field dependent electron relaxation time contribute to the proton correlation time. The fit performed with the SBM theory, without... 

As we see in Chapter 6, surface tension and contact angle measurements provide information on liquid-liquid and solid-liquid adhesion energies (Fig. 1.26c). Contact angles measured under different atmospheric environments or as a function of time provide valuable insights into the states of surfaces and adsorbed films and of molecular reorientation times at interfaces. 

Fig. 4 Dipolar reorientational time correlation function, Cw(t) for bound water molecules in the micellar solution, and for bulk water molecules.

Fig. 8 Reorientational time correlation function of the water dipole, C (<), for water molecules in the three segments of the protein.

The above discussion easily motivates the notion that reorientation times will become long as the liquid is cooled towards the glass transition, but it does not explain the shape of the observed relaxation function. Part of the shear viscosity in fluids is due to coupling to molecular reorientation. This effect has been studied in detail in alkane liquids26,27. At low viscosities the shear modulus can be described by... 

Here td is the so-called Debye dielectric relaxation time. One could view td as a phenomenological time constant which applies to dielectric relaxation measurements, or alternatively for simple causes, involving dielectric relaxation of weakly interacting dipoles, tD is related to the reorientation time constant of the solvent dipole in the laboratory frame. 

The NMR rotational reorientation time of liquid water at 25 °C is 2.5 10-12 sec and the dielectrid relaxation time of liquid water is 8 1(T12 sec173). 

Reorientational times T for water molecules in various adsorbates and in bulk water. 

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